Advanced Studies in Pure Mathematics

New examples of cylindrical Fano fourfolds

Yuri Prokhorov and Mikhail Zaidenberg

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We produce new families of smooth Fano fourfolds with Picard rank 1, which contain cylinders, i.e., Zariski open subsets of form $Z\times{\mathbb A}^1$, where $Z$ is a quasiprojective variety. The affine cones over such a fourfold admit effective $\mathbb{G}_{\operatorname{a}}$-actions. Similar constructions of cylindrical Fano threefolds and fourfolds were done previously in [KPZ11, KPZ14, PZ16].

Article information

Algebraic Varieties and Automorphism Groups, K. Masuda, T. Kishimoto, H. Kojima, M. Miyanishi and M. Zaidenberg, eds. (Tokyo: Mathematical Society of Japan, 2017), 443-463

Received: 8 July 2015
Revised: 12 February 2016
First available in Project Euclid: 21 September 2018

Permanent link to this document euclid.aspm/1537498715

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14R20: Group actions on affine varieties [See also 13A50, 14L30] 14J45: Fano varieties
Secondary: 14J50: Automorphisms of surfaces and higher-dimensional varieties 14R05: Classification of affine varieties

affine cone Fano variety group action additive group


Prokhorov, Yuri; Zaidenberg, Mikhail. New examples of cylindrical Fano fourfolds. Algebraic Varieties and Automorphism Groups, 443--463, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07510443.

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